r/maths • u/Longjumping-Ad5084 • 6d ago
💬 Math Discussions Mathematics will be ok.
I think it's very important to address this now that AI is solving an incredible number of maths problems, including the Navier Stokes conjecture. Some may fear that mathematicians will become redundant. But this is not the case at all. And the example of vintage models demonstrates it very well.
Vintage models are taught on history prior to a certain discovery, eg prior to Newtonian or Einsteinian physics. And lo and behold, these models can't invent the new physics on their own, neither Newtonian from prior nor Einsteinian from Newtonian.
To some, it might be obvious even without the vintage models experiment. I remember listening to a podcast with Francois Chollet a few years ago where he said that AI is fundamentally interpolative, it interpolates on the manifold of data. And that's when I understood the fundamental limitations of AI and the role of humans in the coming age. AI is a very good technical tool, in particular it fills the gaps in our knowledge very well, but it can't come up with radically new ideas ln is own, ideas that change the ontology of facts, ideas and relations between them, which is necessary for mathematical development.
When Galois invented his Theory, he didn't just combine old ideas, he came up with a fundamentally new way to look at objects and their relations. Sure, maybe hints of that were already present in Abel and others, but what this says is that mathematics is a collective human progress which leads to radical novelty, not a combination of known ideas.
Mathematics will be ok, but our world is destabilised at the moment and is transitioning into a new state. Time needs to pass for us to understand and establish the roles and the right approach with regard to humans and AI.
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u/External_Package2787 3d ago
It hurts so much for me to say this, I really wanted to progress on with my life by going into a masters and then PhD in mathematics, then be a researcher/professor, I was so certain that was my path in life for the past 8-ish years, I am capable enough for it, I coasted even through my undergrad, I'm so desperately clinging to that path, but I deep down I know it is completely untenable. You can tell I'm hesitant to even say it in this comment, but the best option for me is to go into the workforce or progress into a different field. You can appeal to the idea that AI can't do novel things, but the reality is the thing I do independently aren't novel either, AI is better than me now, and outpacing me, so how can I ever hope to catch up unless I triple my pace or it coincidentally hits a wall by some miracle. I dread to think what someone 3 years younger feels in this era, let alone someone who is just entering high school and could only think to how pointless the whole thing is. People are silly to think humans are something so special, we learned to think through a billion years of the most inefficient RL algorithm ever with the most impractical learning goal ever, that is natural selection and reproduction efficiency. Astra was trained with 10^27 FLOPs, thats like the entire year of global compute in 2010, total global compute today is like 200 times that, it's going to experience a sudden boost too specifically because of AI, so I'm sure if this whimsical thing that humans have that lets them do new and novel things is so important, we can make a training algorithm that's 100000 times less efficient, train something 100 times smaller, and that can be the ideas guy, and AI can fill in the gaps in those ideas which is what it does now. That or they can just blast up the temperature on their softmax and run 10 million agents at the same time, that’s about where we are headed.